Do Not Forget the Temperature Dependence of the Specific Resistivity!

The discovery of high temperature superconductors
in 1986 immediately lead to proposals to use these materials for
interconnects on chips instead of the Al that was common than (and for
about 15 more years).

The reason was that the finite resistivity of
Al together with parasitic capacitances (e.g. between two conducting
lines on a chip) limits the maximum frequency to

fmax =

1R · C

With R = resistance of the longest connection
line on the chip and C = parasitic capacitance "seen"
by this line.

For R = 0 W as we
have it for a superconductor, the maximum frequency is no longer limited by
R · C, no matter how large the parasitic capacitances are.
Instead, the limit comes from fmax = (L · C)1/2
with L = inductance of the line, and this is just another way of
saying that the signal propagation is limited by the speed of light.

fmax =

(L · C)1/2

Given the resistivity of Al (at room
temperature!), a sizeable advantage was seen for the integrated circuits then
envisioned.

However, comparing the performance of a chip run with
Al at room temperature to a chip run at liquid N2
temperature (77 K), is not the right comparison. After all, you can cool
down the conventional chip, too - and that will decrease
RAl by a factor of 6 - 8.

The comparison then is quite different. The graph shows the
minimum switching time t =
1/fmax as a function of the length of a standard
interconnect line about 1 µm2 cross section.

Whereas superconductors would already make an
interesting difference for lengths of a few mm (typical line length) in
the wrong comparison, the correct
comparison only shows an advantage for about 1 cm and larger - line
lengths easily avoided by clever design.